Longitudinal pattern of basilar membrane vibration in the sensitive cochlea

Localization of the cochlear amplifier in living sensitive ears

Background

To detect soft sounds, the mammalian cochlea increases its sensitivity by amplifying incoming sounds up to one thousand times. Although the cochlear amplifier is thought to be a local cellular process at an area basal to the response peak on the spiral basilar membrane, its location has not been demonstrated experimentally.

Methodology and Principal Findings

Using a sensitive laser interferometer to measure sub-nanometer vibrations at two locations along the basilar membrane in sensitive gerbil cochleae, here we show that the cochlea can boost soft sound-induced vibrations as much as 50 dB/mm at an area proximal to the response peak on the basilar membrane. The observed amplification works maximally at low sound levels and at frequencies immediately below the peak-response frequency of the measured apical location. The amplification decreases more than 65 dB/mm as sound levels increases.

Conclusions and Significance

We conclude that the cochlea amplifier resides at a small longitudinal region basal to the response peak in the sensitive cochlea. These data provides critical information for advancing our knowledge on cochlear mechanisms responsible for the remarkable hearing sensitivity, frequency selectivity and dynamic range.

The biophysical origin of traveling-wave dispersion in the cochlea

Sound processing begins at the peripheral auditory system, where it undergoes a highly complex transformation and spatial separation of the frequency components inside the cochlea. This sensory signal processing constitutes a neurophysiological basis for psychoacoustics. Wave propagation in the cochlea, as shown by measurements of basilar membrane velocity and auditory nerve responses to sound, has demonstrated significant frequency modulation (dispersion), in addition to tonotopic gain and active amplification. The physiological and physical basis for this dispersion remains elusive. In this article, a simple analytical model is presented, along with experimental validation using physiological measurements from guinea pigs, to identify the origin of traveling-wave dispersion in the cochlea. We show that dispersion throughout the cochlea is fundamentally due to the coupled fluid-structure interaction between the basilar membrane and the scala fluids. It is further influenced by the variation in physical and geometrical properties of the basilar membrane, the sensitivity or gain of the hearing organ, and the relative dominance of the compression mode at about one-third octave beyond the best frequency.

Fast reverse propagation of sound in the living cochlea

The auditory sensory organ, the cochlea, not only detects but also generates sounds. Such sounds, otoacoustic emissions, are widely used for diagnosis of hearing disorders and to estimate cochlear nonlinearity. However, the fundamental question of how the otoacoustic emission exits the cochlea remains unanswered. In this study, emissions were provoked by two tones with a constant frequency ratio, and measured as vibrations at the basilar membrane and at the stapes, and as sound pressure in the ear canal. The propagation direction and delay of the emission were determined by measuring the phase difference between basilar membrane and stapes vibrations. These measurements show that cochlea-generated sound arrives at the stapes earlier than at the measured basilar membrane location. Data also show that basilar membrane vibration at the emission frequency is similar to that evoked by external tones. These results conflict with the backward-traveling-wave theory and suggest that at low and intermediate sound levels, the emission exits the cochlea predominantly through the cochlear fluids.

Otoacoustic estimation of cochlear tuning: validation in the chinchilla

We analyze published auditory-nerve and otoacoustic measurements in chinchilla to test a network of hypothesized relationships between cochlear tuning, cochlear traveling-wave delay, and stimulus-frequency otoacoustic emissions (SFOAEs). We find that the physiological data generally corroborate the network of relationships, including predictions from filter theory and the coherent-reflection model of OAE generation, at locations throughout the cochlea. The results support the use of otoacoustic emissions as noninvasive probes of cochlear tuning. Developing this application, we find that tuning ratios-defined as the ratio of tuning sharpness to SFOAE phase-gradient delay in periods-have a nearly species-invariant form in cat, guinea pig, and chinchilla. Analysis of the tuning ratios identifies a species-dependent parameter that locates a transition between "apical-like" and "basal-like" behavior involving multiple aspects of cochlear physiology. Approximate invariance of the tuning ratio allows determination of cochlear tuning from SFOAE delays. We quantify the procedure and show that otoacoustic estimates of chinchilla cochlear tuning match direct measures obtained from the auditory nerve. By assuming that invariance of the tuning ratio extends to humans, we derive new otoacoustic estimates of human cochlear tuning that remain mutually consistent with independent behavioral measurements obtained using different rationales, methodologies, and analysis procedures. The results confirm that at any given characteristic frequency (CF) human cochlear tuning appears sharper than that in the other animals studied, but varies similarly with CF. We show, however, that the exceptionality of human tuning can be exaggerated by the ways in which species are conventionally compared, which take no account of evident differences between the base and apex of the cochlea. Finally, our estimates of human tuning suggest that the spatial spread of excitation of a pure tone along the human basilar membrane is comparable to that in other common laboratory animals.

Compliance profiles derived from a three-dimensional finite-element model of the basilar membrane

A finite-element analysis is used to explore the impact of elastic material properties, boundary conditions, and geometry, including coiling, on the spatial characteristics of the compliance of the unloaded basilar membrane (BM). It is assumed that the arcuate zone is isotropic and the pectinate zone orthotropic, and that the radial component of the effective Young's modulus in the pectinate zone decreases exponentially with distance from base to apex. The results concur with tonotopic characteristics of compliance and neural data. Moreover, whereas the maximum compliance in a radial profile is located close to the boundary between the two zones in the basal region, it shifts to the midpoint of the pectinate zone for the apical BM; the width of the profile also expands. This shift begins near the 1 kHz characteristic place for guinea pig and the 2.4 kHz place for gerbil. Shift and expansion are not observed for linear rather than exponential decrease of the radial component of Young's modulus. This spatial change of the compliance profile leads to the prediction that mechanical excitation in the apical region of the organ of Corti is different to that in the basal region.

In vivo impedance of the gerbil cochlear partition at auditory frequencies

The specific acoustic impedance of the cochlear partition was measured from 4 to 20 kHz in the basal turn of the gerbil cochlea, where the best frequency is approximately 40 kHz. The acoustic impedance was found as the ratio of driving pressure to velocity response. It is the physical attribute that governs cochlear mechanics and has never before been directly measured, to our knowledge. The basilar membrane velocity was measured through the transparent round window membrane. Simultaneously, the intracochlear pressure was measured close to the stapes and quite close to the cochlear partition. The impedance phase was close to -90 degrees and the magnitude decreased with frequency, consistent with stiffness-dominated impedance. The resistive component of the impedance was relatively small. Usually the resistance was negative at frequencies below 8 kHz; this unexpected finding might be due to other vibration modes within the cochlear partition.

Electrically evoked auditory nerve responses in the cochlea with normal outer hair cells

As hybrid cochlear implant devices are increasingly used for restoring hearing in patients with residual hearing it is important to understand electrically evoked responses in cochleae having functional hair cells. To test the hypothesis that extracochlear electrical stimulation (EES) from sinusoidal current can provoke an auditory nerve response with normal frequency selectivity, the EES-evoked compound action potential (ECAP) was investigated in this study. Brief sinusoidal electrical currents, delivered via a round window electrode, were used to evoke ECAP. The ECAP waveform was observed to be the same as the acoustically evoked CAP (ACAP), except for a shorter latency. The input/output and intensity/latency functions of ACAPs and ECAPs were also similar. The maximum acoustic masking for both ACAP and ECAP occurred near probe frequencies. Since the masked tuning curve of a CAP reflects the frequency selectivity of neural excitation, these data demonstrate a highly specific activation of the auditory nerve, which would result in high degree of frequency selectivity. This frequency selectivity likely results from the cochlear traveling wave caused by electrically stimulated outer hair cells.

Functional specialization of medial auditory belt cortex in the alert rhesus monkey

Responses of neural units in two areas of the medial auditory belt (middle medial area [MM] and rostral medial area [RM]) were tested with tones, noise bursts, monkey calls (MC), and environmental sounds (ES) in microelectrode recordings from two alert rhesus monkeys. For comparison, recordings were also performed from two core areas (primary auditory area [A1] and rostral area [R]) of the auditory cortex. All four fields showed cochleotopic organization, with best (center) frequency [BF(c)] gradients running in opposite directions in A1 and MM than in R and RM. The medial belt was characterized by a stronger preference for band-pass noise than for pure tones found medially to the core areas. Response latencies were shorter for the two more posterior (middle) areas MM and A1 than for the two rostral areas R and RM, reaching values as low as 6 ms for high BF(c) in MM and A1, and strongly depended on BF(c). The medial belt areas exhibited a higher selectivity to all stimuli, in particular to noise bursts, than the core areas. An increased selectivity to tones and noise bursts was also found in the anterior fields; the opposite was true for highly temporally modulated ES. Analysis of the structure of neural responses revealed that neurons were driven by low-level acoustic features in all fields. Thus medial belt areas RM and MM have to be considered early stages of auditory cortical processing. The anteroposterior difference in temporal processing indices suggests that R and RM may belong to a different hierarchical level or a different computational network than A1 and MM.

A protective role for type 3 deiodinase, a thyroid hormone-inactivating enzyme, in cochlear development and auditory function

Thyroid hormone is necessary for cochlear development and auditory function, but the factors that control these processes are poorly understood. Previous evidence indicated that in mice, the serum supply of thyroid hormone is augmented within the cochlea itself by type 2 deiodinase, which amplifies the level of T(3), the active form of thyroid hormone, before the onset of hearing. We now report that type 3 deiodinase, a thyroid hormone-inactivating enzyme encoded by Dio3, is expressed in the immature cochlea before type 2 deiodinase. Dio3-/- mice display auditory deficits and accelerated cochlear differentiation, contrasting with the retardation caused by deletion of type 2 deiodinase. The Dio3 mRNA expression pattern in the greater epithelial ridge, stria vascularis, and spiral ganglion partly overlaps with that of thyroid hormone receptor beta (TRbeta), the T(3) receptor that is primarily responsible for auditory development. The proposal that type 3 deiodinase prevents premature stimulation of TRbeta was supported by deleting TRbeta, which converted the Dio3-/- cochlear phenotype from one of accelerated to one of delayed differentiation. The results indicate a protective role for type 3 deiodinase in hearing. The auditory system illustrates the considerable extent to which tissues can autoregulate their developmental response to thyroid hormone through both type 2 and 3 deiodinases.

Pitfalls in behavioral estimates of basilar-membrane compression in humans

Psychoacoustic estimates of basilar-membrane compression often compare on- and off-frequency forward masking. Such estimates involve assuming that the recovery from forward masking for a given signal frequency is independent of masker frequency. To test this assumption, thresholds for a brief 4-kHz signal were measured as a function of masker-signal delay. Comparisons were made between on-frequency (4 kHz) and off-frequency (either 2.4 or 4.4 kHz) maskers, adjusted in level to produce the same amount of masking at a 0-ms delay between masker offset and signal onset. Consistent with the assumption, forward-masking recovery from a moderate-level (83 dB SPL) 2.4-kHz masker and a high-level (92 dB SPL) 4.4-kHz masker was the same as from the equivalent on-frequency maskers. In contrast, recovery from a high-level (92 dB SPL) 2.4-kHz forward masker was slower than from the equivalent on-frequency masker. The results were used to simulate temporal masking curves, taking into account the differences in on- and off-frequency masking recoveries at high levels. The predictions suggest that compression estimates assuming frequency-independent masking recovery may overestimate compression by as much as a factor of 2. The results suggest caution in interpreting forward-masking data in terms of basilar-membrane compression, particularly when high-level maskers are involved.

Variation in the phase of response to low-frequency pure tones in the guinea pig auditory nerve as functions of stimulus level and frequency

The directionality of hair cell stimulation combined with the vibration of the basilar membrane causes the auditory nerve fiber action potentials, in response to low-frequency stimuli, to occur at a particular phase of the stimulus waveform. Because direct mechanical measurements at the cochlear apex are difficult, such phase locking has often been used to indirectly infer the basilar membrane motion. Here, we confirm and extend earlier data from mammals using sine wave stimulation over a wide range of sound levels (up to 90 dB sound pressure level). We recorded phase-locked responses to pure tones over a wide range of frequencies and sound levels of a large population of auditory nerve fibers in the anesthetized guinea pig. The results indicate that, for a constant frequency of stimulation, the phase lag decreases with increases in the characteristic frequency (CF) of the nerve fiber. The phase lag decreases up to a CF above the stimulation frequency, beyond which it decreases at a much slower rate. Such phase changes are consistent with known basal cochlear mechanics. Measurements from individual fibers showed smaller but systematic variations in phase with sound level, confirming previous reports. We found a "null" stimulation frequency at which little variation in phase occurred with sound level. This null frequency was often not at the CF. At stimulation frequencies below the null, there was a progressive lag with sound level and a progressive lead for stimulation frequencies above the null. This was maximally 0.2 cycles.

Can the binaural system extract fine-structure interaural time differences from noncorresponding frequency channels?

Due to the phase differences in the basilar membrane response between neighboring places along the cochlea, it is generally assumed that the processing of interaural time differences (ITDs) in the temporal fine structure relies on comparisons between corresponding frequency channels from the two ears. This study was aimed to test whether the auditory system is capable of extracting fine-structure ITDs from noncorresponding channels. For that, the ITD discrimination threshold was measured for a 500 Hz pure tone partially masked by a lowpass masker in one ear and a highpass masker in the other. The maskers were intended to obscure the apical or basal part of the tone's excitation pattern, respectively, and thus force the listener to extract ITDs from disparate channels. While the results did not allow any definite conclusions as to whether or not ITD processing in these conditions was based on cross-channel comparisons, some aspects of the data suggest that it was. Modeling simulations showed that any cross-channel comparisons would have to be limited to a fairly narrow frequency range of little more than one auditory-filter bandwidth. However, the between-channel phase differences within even such a narrow range would be sufficient to explain ITD sensitivity in neurophysiological data.

Effect of the cochlear microphonic on the limiting frequency of the mammalian ear

Electromotility is a basis for cochlear amplifier, which controls the sensitivity of the mammalian ear and contributes to its frequency selectivity. Because it is driven by the receptor potential, its frequency characteristics are determined by the low-pass RC filter intrinsic to the cell, which has a corner frequency about 1/10th of the operating frequency. This filter significantly decreases the efficiency of electromotility as an amplifier. The present paper examines a proposal that the cochlear microphonic, the voltage drop across the extracellular medium by the receptor current, contributes to overcome this problem. It is found that this effect can improve frequency dependence. However, this effect alone is too small to enhance the effectiveness of electromotility beyond 10 kHz in the mammalian ear.

Reverse wave propagation in the cochlea

Otoacoustic emissions, sounds generated by the inner ear, are widely used for diagnosing hearing disorders and studying cochlear mechanics. However, it remains unclear how emissions travel from their generation sites to the cochlear base. The prevailing view is that emissions reach the cochlear base via a backward-traveling wave, a slow-propagating transverse wave, along the cochlear partition. A different view is that emissions propagate to the cochlear base via the cochlear fluids as a compressional wave, a fast longitudinal wave. These theories were experimentally tested in this study by measuring basilar membrane (BM) vibrations at the cubic distortion product (DP) frequency from two longitudinal locations with a laser interferometer. Generation sites of DPs were varied by changing frequencies of primary tones while keeping the frequency ratio constant. Here, we show that BM vibration amplitude and phase at the DP frequency are very similar to responses evoked by external tones. Importantly, the BM vibration phase at a basal location leads that at a more apical location, indicating a traveling wave that propagates in the forward direction. These data are in conflict with the backward- traveling-wave theory but are consistent with the idea that the emission comes out of the cochlea predominantly through compressional waves in the cochlear fluids.

Laser amplification with a twist: traveling-wave propagation and gain functions from throughout the cochlea

Except at the handful of sites explored by the inverse method, the characteristics-indeed, the very existence-of traveling-wave amplification in the mammalian cochlea remain largely unknown. Uncertainties are especially pronounced in the apex, where mechanical and electrical measurements lack the independent controls necessary for assessing damage to the preparation. At a functional level, the form and amplification of cochlear traveling waves are described by quantities known as propagation and gain functions. A method for deriving propagation and gain functions from basilar-membrane mechanical transfer functions is presented and validated by response reconstruction. Empirical propagation and gain functions from locations throughout the cochlea are obtained in mechanically undamaged preparations by applying the method to published estimates of near-threshold basilar membrane responses derived from Wiener-kernel (chinchilla) and zwuis analysis (cat) of auditory-nerve responses to broadband stimuli. The properties of these functions, and their variation along the length of the cochlea, are described. In both species, and at all locations examined, the gain functions reveal a region of positive power gain basal to the wave peak. The results establish the existence of traveling-wave amplification throughout the cochlea, including the apex. The derived propagation and gain functions resemble those characteristic of an active optical medium but rotated by 90 degrees in the complex plane. Rotation of the propagation and gain functions enables the mammalian cochlea to operate as a wideband, hydromechanical laser analyzer.

The role of organ of Corti mass in passive cochlear tuning

The mechanism for passive cochlear tuning remains unsettled. Early models considered the organ of Corti complex (OCC) as a succession of spring-mass resonators. Later, traveling wave models showed that passive tuning could arise through the interaction of cochlear fluid mass and OCC stiffness without local resonators. However, including enough OCC mass to produce local resonance enhanced the tuning by slowing and thereby growing the traveling wave as it approached its resonant segment. To decide whether the OCC mass plays a role in tuning, the frequency variation of the wavenumber of the cochlear traveling wave was measured (in vivo, passive cochleae) and compared to theoretical predictions. The experimental wavenumber was found by taking the phase difference of basilar membrane motion between two longitudinally spaced locations and dividing by the distance between them. The theoretical wavenumber was a solution of the dispersion relation of a three-dimensional cochlear model with OCC mass and stiffness as the free parameters. The experimental data were only well fit by a model that included OCC mass. However, as the measurement position moved from a best-frequency place of 40 to 12 kHz, the role of mass was diminished. The notion of local resonance seems to only apply in the very high-frequency region of the cochlea.

Modeling of Sound Transmission from Ear Canal to Cochlea

A 3-D finite element (FE) model of the human ear consisting of the external ear canal, middle ear, and cochlea is reported in this paper. The acoustic-structure-fluid coupled FE analysis was conducted on the model which included the air in the ear canal and middle ear cavity, the fluid in the cochlea, and the middle ear and cochlea structures (i.e., bones and soft tissues). The middle ear transfer function such as the movements of tympanic membrane, stapes footplate, and round window, the sound pressure gain across the middle ear, and the cochlear input impedance in response to sound stimulus applied in the ear canal were derived and compared with the published experimental measurements in human temporal bones. The frequency sensitivity of the basilar membrane motion and intracochlear pressure induced by sound pressure in the ear canal was predicted along the length of the basilar membrane from the basal turn to the apex. The satisfactory agreements between the model and experimental data in the literature indicate that the middle ear function was well simulated by the model and the simplified cochlea was able to correlate sound stimulus in the ear canal with vibration of the basilar membrane and pressure variation of the cochlear fluid. This study is the first step toward the development of a comprehensive FE model of the entire human ear for acoustic-mechanical analysis.

A mechanism for active hearing

The remarkable sensitivity, frequency selectivity, and nonlinearity of the cochlea have been attributed to the putative 'cochlear amplifier', which consumes metabolic energy to amplify the cochlear mechanical response to sounds. Recent studies have demonstrated that outer hair cells actively generate force using somatic electromotility and active hair-bundle motion. However, the expected power gain of the cochlear amplifier has not been demonstrated experimentally, and the measured location of cochlear nonlinearity is inconsistent with the predicted location of the cochlear amplifier. We instead propose a 'cochlear transformer' mechanism to interpret cochlear performance.

Altered traveling wave propagation and reduced endocochlear potential associated with cochlear dysplasia in the BETA2/NeuroD1 null mouse

The BETA2/NeuroD1 null mouse has cochlear dysplasia. Its cochlear duct is shorter than normal, there is a lack of spiral ganglion neurons, and there is hair cell disorganization. We measured vertical movements of the tectorial membrane at acoustic frequencies in excised cochleae in response to mechanical stimulation of the stapes using laser doppler vibrometry. While tuning curve sharpness was similar between wild-type, heterozygotes, and null mice in the base, null mutants had broader tuning in the apex. At both the base and the apex, null mice had less phase lag accumulation with increasing stimulus frequency than wild-type or heterozygote mice. In vivo studies demonstrated that the null mouse lacked distortion product otoacoustic emissions, and the cochlear microphonic and endocochlear potential were found to be severely reduced. Electrically evoked otoacoustic emissions could be elicited, although the amplitudes were lower than those of wild-type mice. Cochlear cross-sections revealed an incomplete partition malformation, with fenestrations within the modiolus that connected the cochlear turns. Outer hair cells from null mice demonstrated the normal pattern of prestin expression within their lateral walls and normal FM 1-43 dye entry. Overall, these data demonstrate that while tonotopicity can exist with cochlear dysplasia, traveling wave propagation is abnormally fast. Additionally, the presence of electrically evoked otoacoustic emissions suggests that outer hair cell reverse transduction is present, although the acoustic response is shaped by the alterations in cochlear mechanics.

Similarity of traveling-wave delays in the hearing organs of humans and other tetrapods

Transduction of sound in mammalian ears is mediated by basilar-membrane waves exhibiting delays that increase systematically with distance from the cochlear base. Most contemporary accounts of such “traveling-wave” delays in humans have ignored postmortem basilar-membrane measurements in favor of indirect in vivo estimates derived from brainstem-evoked responses, compound action potentials, and otoacoustic emissions. Here, we show that those indirect delay estimates are either flawed or inadequately calibrated. In particular, we argue against assertions based on indirect estimates that basilar-membrane delays are much longer in humans than in experimental animals. We also estimate in vivo basilar-membrane delays in humans by correcting postmortem measurements in humans according to the effects of death on basilar-membrane vibrations in other mammalian species. The estimated in vivo basilar-membrane delays in humans are similar to delays in the hearing organs of other tetrapods, including those in which basilar membranes do not sustain traveling waves or that lack basilar membranes altogether.

Two-tone distortion at different longitudinal locations on the basilar membrane

When listening to two tones at frequency f1 and f2 (f2>f1), one can hear pitches not only at f1 and f2 but also at distortion frequencies f2-f1, (n+1)f1-nf2, and (n+1)f2-nf1 (n=1,2,3...). Such two-tone distortion products (DPs) also can be measured in the ear canal using a sensitive microphone. These ear-generated sounds are called otoacoustic emissions (OAEs). In spite of the common applications of OAEs, the mechanisms by which these emissions travel out of the cochlea remain unclear. In a recent study, the basilar membrane (BM) vibration at 2f1-f2 was measured as a function of the longitudinal location, using a scanning laser interferometer. The data indicated a forward traveling wave and no measurable backward wave. However, this study had a relatively high noise floor and high stimulus intensity. In the current study, the noise floor of the BM measurement was significantly decreased by using reflective beads on the BM, and the vibration was measured at relatively low intensities at more than one longitudinal location. The results show that the DP phase at a basal location leads the phase at an apical location. The data indicate that the emission travels along the BM from base to apex as a forward traveling wave, and no backward traveling wave was detected under the current experimental conditions.

Panoramic measurements of the apex of the cochlea

Our understanding of cochlear mechanics is impeded by the lack of truly panoramic data. Sensitive mechanical measurements cover only a narrow cochlear region, mostly in the base. The global spatiotemporal pattern of vibrations along the cochlea cannot be inferred from such local measurements but is often extrapolated beyond the measurement spot under the assumption of scaling invariance. Auditory nerve responses give an alternative window on the entire cochlea, but traditional techniques do not allow recovery of the effective vibration pattern. We developed a new analysis technique to measure cochlear amplitude and phase transfer of fibers with characteristic frequencies <5 kHz. Data from six cats yielded panoramic phase profiles along the apex of the cochlea for an approximately 5 octave range of stimulus frequencies. All profiles accumulated systematic phase lags from base to apex. Phase accumulation was not gradual but showed a two-segment character: a steep segment (slow propagation) around the characteristic position of the stimulus, and a shallow segment (fast propagation) basal to it. The transition between the segments occurred in a narrow region and was smooth. Wavelength near characteristic position decreased from approximately 3.5 to approximately 1 mm for frequencies from 200 to 4000 Hz, corresponding to phase velocities of approximately 0.5 to approximately 5 m/s. The accumulated phase lag between the eardrum and characteristic position varied from approximately 1 cycle at 200 Hz to approximately 2.5 cycle at 4 kHz, invalidating scaling invariance. The generic character of our analysis technique and its success in solving the difficult problem of reconstructing the effective sensory input from neural recordings suggest its wider application as a powerful alternative to customary system analysis techniques.

Group Delay of Acoustic Emissions in the Ear

It is commonly accepted that the cochlea emits sound by a backward traveling wave along the cochlear partition. This belief is mainly based on an observation that the group delay of the otoacoustic emission measured in the ear canal is twice as long as the forward delay. In this study, the otoacoustic emission was measured in the gerbil under anesthesia not only in the ear canal but also at the stapes, eliminating measurement errors arising from unknown external- and middle-ear delays. The emission group delay measured at the stapes was compared with the group delay of basilar membrane vibration at the putative emission-generation site, the forward delay. The results show that the total intracochlear delay of the emission is equal to or smaller than the forward delay. For emissions with an f2/f1 ratio <1.2, the data indicate that the reverse propagation of the emission from its generation site to the stapes is much faster than a forward traveling wave to the f2 location. In addition, that the round-trip delays are smaller than the forward delay implies a basal shift of the emission generation site, likely explained by the basal shift of primary-tone response peaks with increasing intensity. However, for emissions with an f1 ≪ f2, the data cannot distinguish backward traveling waves from compression waves because of a very small f1 delay at the f2 site.

Doppler optical coherence microscopy for studies of cochlear mechanics

The possibility of measuring subnanometer motions with micron scale spatial resolution in the intact mammalian cochlea using Doppler optical coherence microscopy (DOCM) is demonstrated. A novel DOCM system is described that uses two acousto-optic modulators to generate a stable 500-kHz heterodyne frequency. Images and motion measurements are obtained using phase-resolved analysis of the interference signal. The DOCM system permits imaging with micron-scale resolution and 85-dB sensitivity and motion measurements with 100-kHz bandwidth, directional discrimination, and 30-pm/Hz(0.5) noise floor. Images and motion measurements are presented that demonstrate the ability to resolve motions of structures of interest in a mammalian cochlea in vitro including the basilar membrane, reticular lamina, tectorial membrane, and outer hair cells.

Local mechanical stimulation of the hearing organ by laser irradiation

Light produces force when interacting with matter. Such radiation pressure may be used to accelerate small objects along the beam path of a laser. Here, we demonstrate that a moderately powerful laser can deliver enough force to locally stimulate the hearing organ, in the absence of conventional sound. Damped mechanical oscillations are observed following brief laser pulses, implying that the organ of Corti is locally resonant. This new method will be helpful for probing the mechanical properties of the hearing organ, which have crucial importance for the ear's ability to detect sound.

Distortion-product otoacoustic emission spectra and high-resolution audiometry in noise-induced hearing loss

Distortion product otoacoustic emissions (DPOAE) elicited by 60dB SPL pure tones at f1 and f2 were collected at 2f1-f2, in 1/10th octave steps, in a sample of 36 ears from 27 patients with noise-induced hearing loss (NIHL). They were analyzed in the frequency domain against the outcome of high-resolution pure-tone audiometry, performed with the help of a Békésy sweep-frequency automatic audiometer. The characteristics of DPOAE level plots as a function of frequency (the so-called DP-grams), relative to the DPOAE levels of a control age-matched group, were compared to their alleged counterparts on the audiograms, i.e., the lower and upper frequency boundaries of the interval with hearing loss. Ears with NIHL split into two subgroups, one (n = 25) with a notch in the DP-gram such that its lower boundary matched the lower limit of the audiometric notch (linear regression with a slope of 0.91, r(2) = 0.644, p < 0.001). Likewise, when it existed, its upper boundary matched its upper counterpart on the audiogram (linear regression with a slope of 0.96, r(2) = 0.89, p < 0.001). In this respect, DP-grams performed better than transient-evoked OAE spectra, which exhibited poor correlations with audiogram patterns. The second subgroup (n = 11) exhibited normal DPOAEs at all frequencies despite audiometric losses similar to those of the first subgroup. In all cases, DPOAE levels were poor predictors of the degree of hearing losses. It is hypothesized that NIHL in the second subgroup involves inner hair cells or auditory neurons, instead of outer hair cells in the first subgroup. Provided NIHL affected outer hair cells, DP-grams provided a comparatively accurate predictor of the spectral extent of hearing loss.

Compression, adaptation and efferent control in a revised outer hair cell functional model

In the cochlea of the inner ear, outer hair cells (OHC) together with the local passive structures of the tectorial and basilar membranes comprise non-linear resonance circuits with the local and central (afferent-efferent) feedback. The characteristics of these circuits and their control possibilities depend on the mechanomotility of the OHC. The main element of our functional model of the OHC is the mechanomotility circuit with the general transfer characteristic y=ktanh(x-a). The parameter k of this characteristic reflects the axial stiffness of the OHC, and the parameter a working position of the hair bundle. The efferent synaptic signals act on the parameter k directly and on the parameter a indirectly through changes in the membrane potential. The dependences of the sensitivity and selectivity on changes in the parameters a and k are obtained by the computer simulation. Functioning of the model at low-level input signals is linear. Due to the non-linearity of the transfer characteristic of the mechanomotility circuit the high-level signals are compressed. For the adaptation and efferent control, however, the transfer characteristic with respect to the initial operating point should be asymmetrical (a>0). The asymmetry relies on the deflection of the hair bundle from the axis of the OHC.

Two modes of motion of the alligator lizard cochlea: measurements and model predictions

Measurements of motion of an in vitro preparation of the alligator lizard basilar papilla in response to sound demonstrate elliptical trajectories. These trajectories are consistent with the presence of both a translational and rotational mode of motion. The translational mode is independent of frequency, and the rotational mode has a displacement peak near 5 kHz. These measurements can be explained by a simple mechanical system in which the basilar papilla is supported asymmetrically on the basilar membrane. In a quantitative model, the translational admittance is compliant while the rotational admittance is second order. Best-fit model parameters are consistent with estimates based on anatomy and predict that fluid flow across hair bundles is a primary source of viscous damping. The model predicts that the rotational mode contributes to the high-frequency slopes of auditory nerve fiber tuning curves, providing a physical explanation for a low-pass filter required in models of this cochlea. The combination of modes makes the sensitivity of hair bundles more uniform with radial position than that which would result from pure rotation. A mechanical analogy with the organ of Corti suggests that these two modes of motion may also be present in the mammalian cochlea.

Perception of spectral contrast by hearing-impaired listeners

The ability to discriminate the spectral shapes of complex sounds is critical to accurate speech perception. Part of the difficulty experienced by listeners with hearing loss in understanding speech sounds in noise may be related to a smearing of the internal representation of the spectral peaks and valleys because of the loss of sensitivity and an accompanying reduction in frequency resolution. This study examined the discrimination by hearing-impaired listeners of highly similar harmonic complexes with a single spectral peak located in 1 of 3 frequency regions. The minimum level difference between peak and background harmonics required to discriminate a small change in the spectral center of the peak was measured for peaks located near 2, 3, or 4 kHz. Component phases were selected according to an algorithm thought to produce either highly modulated (positive Schroeder) or very flat (negative Schroeder) internal waveform envelopes in the cochlea. The mean amplitude difference between a spectral peak and the background components required for discrimination of pairs of harmonic complexes (spectral contrast threshold) was from 4 to 19 dB greater for listeners with hearing impairment than for a control group of listeners with normal hearing. In normal-hearing listeners, improvements in threshold were seen with increasing stimulus level, and there was a strong effect of stimulus phase, as the positive Schroeder stimuli always produced lower thresholds than the negative Schroeder stimuli. The listeners with hearing loss showed no consistent spectral contrast effects due to stimulus phase and also showed little improvement with increasing stimulus level, once their sensitivity loss was overcome. The lack of phase and level effects may be a result of the more linear processing occurring in impaired ears, producing poorer-than-normal frequency resolution, a loss of gain for low amplitudes, and an altered cochlear phase characteristic in regions of damage.

Coherent reflection in a two-dimensional cochlea: Short-wave versus long-wave scattering in the generation of reflection-source otoacoustic emissions

The theory of coherent reflection filtering explains the empirical form of the cochlear reflectance by showing how it emerges from the coherent "backscattering" of forward-traveling waves by impedance perturbations in the mechanics of the cochlear partition. Since the theory was developed using the one-dimensional (1-D) transmission-line model of the cochlea, an obvious logical shortcoming is the failure of the long-wavelength approximation near the peak of the traveling wave, where coherent backscattering is purported to occur. Indeed, existing theory suggests that wave reflection may be strongly suppressed in the short-wave regime. To understand how short-wave behavior near the peak modifies the predictions of the long-wave theory, this paper solves the scattering problem in the 2-D cochlear model. The 2-D problem is reduced to a 1-D wave equation and the solution expressed as an infinite series in which successive terms arise via multiple scattering within the cochlea. The cochlear reflectance is computed in response-matched models constructed by solving the inverse problem to control for variations in mechanical tuning among models of different heights and dimensionality. Reflection from the peak region is significantly enhanced by the short-wave hydrodynamics, but other conclusions of the 1-D analysis--such as the predicted relation between emission group delay and the wavelength of the traveling wave--carry over with only minor modifications. The results illustrate the important role of passive hydromechanical effects in shaping otoacoustic emissions and cochlear tuning.

Organ of Corti potentials and the motion of the basilar membrane

During sound stimulation, receptor potentials are generated within the sensory hair cells of the cochlea. Prevailing theory states that outer hair cells use the potential-sensitive motor protein prestin to convert receptor potentials into fast alterations of cellular length or stiffness that boost hearing sensitivity almost 1000-fold. However, receptor potentials are attenuated by the filter formed by the capacitance and resistance of the membrane of the cell. This attenuation would limit cellular motility at high stimulus frequencies, rendering the above scheme ineffective. Therefore, Dallos and Evans (1995a) proposed that extracellular potential changes within the organ of Corti could drive cellular motor proteins. These extracellular potentials are not filtered by the membrane. To test this theory, both electric potentials inside the organ of Corti and basilar membrane vibration were measured in response to acoustic stimulation. Vibrations were measured at sites very close to those interrogated by the recording electrode using laser interferometry. Close comparison of the measured electrical and mechanical tuning curves and time waveforms and their phase relationships revealed that those extracellular potentials indeed could drive outer hair cell motors. However, to achieve the sharp frequency tuning that characterizes the basilar membrane, additional mechanical processing must occur inside the organ of Corti.

Tympanal travelling waves in migratory locusts

Hearing animals, including many vertebrates and insects, have the capacity to analyse the frequency composition of sound. In mammals, frequency analysis relies on the mechanical response of the basilar membrane in the cochlear duct. These vibrations take the form of a slow vibrational wave propagating along the basilar membrane from base to apex. Known as von Békésy's travelling wave, this wave displays amplitude maxima at frequency-specific locations along the basilar membrane, providing a spatial map of the frequency of sound--a tonotopy. In their structure, insect auditory systems may not be as sophisticated at those of mammals, yet some are known to perform sound frequency analysis. In the desert locust, this analysis arises from the mechanical properties of the tympanal membrane. In effect, the spatial decomposition of incident sound into discrete frequency components involves a tympanal travelling wave that funnels mechanical energy to specific tympanal locations, where distinct groups of mechanoreceptor neurones project. Notably, observed tympanal deflections differ from those predicted by drum theory. Although phenomenologically equivalent, von Békésy's and the locust's waves differ in their physical implementation. von Békésy's wave is born from interactions between the anisotropic basilar membrane and the surrounding incompressible fluids, whereas the locust's wave rides on an anisotropic membrane suspended in air. The locust's ear thus combines in one structure the functions of sound reception and frequency decomposition.

Do forward- and backward-traveling waves occur within the cochlea? Countering the critique of Nobili et al

The question of whether or not forward- and backward-traveling waves occur within the cochlea constitutes a long-standing controversy in cochlear mechanics recently brought to the fore by the problem of understanding otoacoustic emissions. Nobili and colleagues articulate the opposition to the traveling-wave viewpoint by arguing that wave-equation formulations of cochlear mechanics fundamentally misrepresent the hydrodynamics of the cochlea [e.g., Nobili et al. (2003) J. Assoc. Res. Otolaryngol. 4:478-494]. To correct the perceived deficiencies of the wave-equation formulation, Nobili et al. advocate an apparently altogether different approach to cochlear modeling--the so-called "hydrodynamic" or "Green's function" approach--in which cochlear responses are represented not as forward- and backward-traveling waves but as weighted sums of the motions of individual basilar membrane oscillators, each interacting with the others via forces communicated instantaneously through the cochlear fluids. In this article, we examine Nobili and colleagues' arguments and conclusions while attempting to clarify the broader issues at stake. We demonstrate that the one-dimensional wave-equation formulation of cochlear hydrodynamics does not misrepresent long-range fluid coupling in the cochlea, as claimed. Indeed, we show that the long-range component of Nobili et al.'s three-dimensional force propagator is identical to the hydrodynamic Green's function representing a one-dimensional tapered transmission line. Furthermore, simulations that Nobili et al. use to discredit wave-equation formulations of cochlear mechanics (i.e., cochlear responses to excitation at a point along the basilar membrane) are readily reproduced and interpreted using a simple superposition of forward- and backward-traveling waves. Nobili and coworkers' critique of wave-equation formulations of cochlear mechanics thus appears to be without compelling foundation. Although the traveling-wave and hydrodynamic formulations impose strikingly disparate conceptual and computational frameworks, the two approaches ultimately describe the same underlying physics.

Frequency specificity of distortion-product otoacoustic emissions produced by high-level tones despite inefficient cochlear electromechanical feedback

Distortion product otoacoustic emissions (DPOAEs) are thought to stem from the outer hair cells (OHCs) around the normally narrow place tuned to the primary tone stimuli. They are thus said to be frequency-specific: their local absence should accurately pinpoint local OHC damage. Yet the influence of impaired tuning on DPOAE frequency specificity is poorly documented. Mice with local damage to OHCs were examined. Their DPOAEs were frequency-specific in that audiometric notches were accurately tracked. The same cochleae were further impaired by ischemia or furosemide injection inducing strial dysfunction with flat loss of sensitivity and tuning, while the preexisting pattern of damaged OHCs remained unaltered. Despite the loss of cochlear activity, DPOAEs produced by high-level (> or =70 dB SPL) primaries remained large in about the same interval where they had been initially normal, i.e., that with nondamaged OHCs, albeit with a slight frequency shift, of -1.1 kHz on average. Thus, the ability of DPOAEs to map structurally intact OHCs cannot be a mere consequence of cochlear tuning as it largely persists in its absence. The key element for this correct mapping is likely part of intact OHC structures (e.g., stereocilia bundles) and must have some tuning of its own.

Semicircular canal fenestration - improvement of bone- but not air-conducted auditory thresholds

Auditory stimulation can, under certain circumstances, activate the vestibular end organs and this is facilitated by fenestration of a semicircular canal (SCC). Several fenestrated profoundly deaf patients reported improvements in their bone- (BC) but not air-conducted (AC) thresholds. Bone conduction auditory thresholds have been reported to be better than normal in several patients with thinning or absence of bone over a SCC (dehiscence). This phenomenon was carefully studied in the fat sand rat (Psammomys obesus) by recording auditory brainstem evoked responses to BC and AC auditory stimulation, before and after SCC fenestration. Fenestration would be expected to decrease the pressure difference across the cochlear partition, causing a reduction in the amplitude of the classical base to apex input traveling wave, and should therefore lead to an elevation in AC and BC thresholds. Instead, BC thresholds decreased (i.e. improved) following fenestration (by 7.0+/-4.2 dB; P<0.005), while AC thresholds did not change. Thus the cochlea becomes more sensitive to BC, but not AC, stimulation in the presence of a SCC fenestration. This may be due to the removal by the fenestration of a factor impeding BC cochlear responses, or by the addition of a facilitating factor. The result that the SCC fenestration did not affect AC threshold provides support for the concept that at low intensities the outer hair cells are directly activated by components of the fluid pressures surrounding them, which alternate at audio-frequencies. These cochlear fluid audio-frequency pressures are induced by stapes footplate movement and not by a base to apex input traveling wave. The audio-frequency pressures would not be affected by SCC fenestration. The outer hair cell motility thus induced somehow excites the inner hair cells and the auditory nerve fibers. At low intensities the outer hair cell motility causes localized displacement at the appropriate position on the basilar membrane.

Prediction of the characteristics of two types of pressure waves in the cochlea: theoretical considerations

The aim of this study was to predict the characteristics of two types of cochlear pressure waves, so-called fast and slow waves. A two-dimensional finite-element model of the organ of Corti (OC), including fluid-structure interaction with the surrounding lymph fluid, was constructed. The geometry of the OC at the basal turn was determined from morphological measurements of others in the gerbil hemicochlea. As far as mechanical properties of the materials within the OC are concerned, previously determined mechanical properties of portions within the OC were adopted, and unknown mechanical features were determined from the published measurements of static stiffness. Time advance of the fluid-structure scheme was achieved by a staggered approach. Using the model, the magnitude and phase of the fast and slow waves were predicted so as to fit the numerically obtained pressure distribution in the scala tympani with what is known about intracochlear pressure measurement. When the predicted pressure waves were applied to the model, the numerical result of the velocity of the basilar membrane showed good agreement with the experimentally obtained velocity of the basilar membrane documented by others. Thus, the predicted pressure waves appeared to be reliable. Moreover, it was found that the fluid-structure interaction considerably influences the dynamic behavior of the OC at frequencies near the characteristic frequency.

Evidence of tectorial membrane radial motion in a propagating mode of a complex cochlear model

Knowledge of vibratory patterns in the cochlea is crucial to understanding the stimulation of mechanosensory cells. Experiments to determine the motion of the cochlear partition and surrounding fluid are extremely challenging. As a result, the motion data are incomplete and often contradictory. The bending mechanism of hair bundles, thought to be related to the shear motion and endolymphatic flow between the tectorial membrane (TM) and reticular lamina (RL), is controversial. We, therefore, extend the frequency range of our previous hybrid analytical-finite-element approach to model the basal as well as apical regions of the guinea pig cochlea. We solve the fluid-solid interaction eigenvalue problem for the axial wavenumber, fluid pressure, and vibratory relative motions of the cochlear partition as a function of frequency. A simple monophasic vibratory mode of the basilar membrane is found at both ends of the cochlea. However, this simple movement is associated with a complex frequency-dependent relative deformation between the TM and the RL. We provide evidence of a radial component of TM motion that is out of phase with the RL and that facilitates the bending of outer hair cell stereocilia at appropriate frequencies at both the cochlear base and apex.

Reverse propagation of sound in the gerbil cochlea

It is commonly believed that the cochlea emits sounds through backward-traveling waves. In the present experiment using a scanning-laser interferometer, I detected forward-traveling but not backward-traveling waves and found that the stapes vibrates earlier than the basilar membrane. These results contradict the current theory and show that the ear emits sounds through the cochlear fluids as compression waves rather than along the basilar membrane as backward-traveling waves.

Harmonic distortion in intracochlear pressure and its analysis to explore the cochlear amplifier

Intracochlear pressure was measured close to the basal basilar membrane in gerbil with pure-tone stimulation. This report describes harmonic distortion in the pressure. The harmonic components were tuned in frequency and physiologically vulnerable, implying that they were related to the cell-derived force that sharpens tuning at low levels in healthy cochleae. For stimulus frequencies in the vicinity of the best frequency the harmonic distortion appeared to be produced locally, at the place of measurement. Therefore, it could be explored with a local nonlinear model. The combined model and observations demonstrate two specific points: First, the harmonics in the cell-based force were likely similar in size to the harmonics in pressure (multiplied by area) close to the basilar membrane. This is distinctly different than the situation for the fundamental component, where the cell-based force is apparently much smaller than the pressure (times area). Second, although the fundamental component of the measured pressure was much larger than its harmonic components, the harmonic and fundamental components of the active force were likely much more similar in size. This allows the harmonic components in the pressure to be used as an indirect measure of the active force.

Low magnitude mechanical loading is osteogenic in children with disabling conditions

The osteogenic potential of short durations of low-level mechanical stimuli was examined in children with disabling conditions. The mean change in tibia vTBMD was +6.3% in the intervention group compared with -11.9% in the control group. This pilot randomized controlled trial provides preliminary evidence that low-level mechanical stimuli represent a noninvasive, non-pharmacological treatment of low BMD in children with disabling conditions.

INTRODUCTION

Recent animal studies have demonstrated the anabolic potential of low-magnitude, high-frequency mechanical stimuli to the trabecular bone of weight-bearing regions of the skeleton. The main aim of this prospective, double-blind, randomized placebo-controlled pilot trial (RCT) was to examine whether these signals could effectively increase tibial and spinal volumetric trabecular BMD (vTBMD; mg/ml) in children with disabling conditions.

MATERIALS AND METHODS

Twenty pre-or postpubertal disabled, ambulant, children (14 males, 6 females; mean age, 9.1 +/- 4.3 years; range, 4-19 years) were randomized to standing on active (n = 10; 0.3g, 90 Hz) or placebo (n = 10) devices for 10 minutes/day, 5 days/week for 6 months. The primary outcomes of the trial were proximal tibial and spinal (L2) vTBMD (mg/ml), measured using 3-D QCT. Posthoc analyses were performed to determine whether the treatment had an effect on diaphyseal cortical bone and muscle parameters.

RESULTS AND CONCLUSIONS

Compliance was 44% (4.4 minutes per day), as determined by mean time on treatment (567.9 minutes) compared with expected time on treatment over the 6 months (1300 minutes). After 6 months, the mean change in proximal tibial vTBMD in children who stood on active devices was 6.27 mg/ml (+6.3%); in children who stood on placebo devices, vTBMD decreased by -9.45 mg/ml (-11.9%). Thus, the net benefit of treatment was +15.72 mg/ml (17.7%; p = 0.0033). In the spine, the net benefit of treatment, compared with placebo, was +6.72 mg/ml, (p = 0.14). Diaphyseal bone and muscle parameters did not show a response to treatment. The results of this pilot RCT have shown for the first time that low-magnitude, high-frequency mechanical stimuli are anabolic to trabecular bone in children, possibly by providing a surrogate for suppressed muscular activity in the disabled. Over the course of a longer treatment period, harnessing bone's sensitivity to these stimuli may provide a non-pharmacological treatment for bone fragility in children.

Cochlear activation at low sound intensities by a fluid pathway

In order to assess the mechanisms responsible for cochlear activation at low sound intensities, a semi-circular canal was fenestrated in fat sand rats, and in other experiments a hole was made in the bone over the scala vestibuli of the first turn of the guinea-pig cochlea. Such holes, which expose the cochlear fluids to air, provide a sound pathway out of the cochlea which is of lower impedance than that through the round window. This should attenuate the pressure difference across the cochlear partition and thereby reduce the driving force for the base-to-apex traveling wave along the basilar membrane. The thresholds of the auditory nerve brainstem evoked responses (ABR) and of the cochlear microphonic potentials were not affected in the fenestration experiments. In addition, holes in the scala vestibuli of the first turn did not cause ABR threshold elevations. These results contribute further evidence that at low sound intensities the outer hair cells are probably not activated by a base-to-apex traveling wave along the basilar membrane. Instead it is possible that they are excited directly by the alternating condensation/rarefaction fluid pressures induced by the vibrations of the stapes footplate. The activated outer hair cells would then cause the localized basilar membrane movement.

Otoacoustic emissions from residual oscillations of the cochlear basilar membrane in a human ear model

Sounds originating from within the inner ear, known as otoacoustic emissions (OAEs), are widely exploited in clinical practice but the mechanisms underlying their generation are not entirely clear. Here we present simulation results and theoretical considerations based on a hydrodynamic model of the human inner ear. Simulations show that, if the cochlear amplifier (CA) gain is a smooth function of position within the active cochlea, filtering performed by a middle ear with an irregular, i.e., nonsmooth, forward transfer function suffices to produce irregular and long-lasting residual oscillations of cochlear basilar membrane (BM) at selected frequencies. Feeding back to the middle ear through hydrodynamic coupling afforded by the cochlear fluid, these oscillations are detected as transient evoked OAEs in the ear canal. If, in addition, the CA gain profile is affected by irregularities, residual BM oscillations are even more irregular and tend to evolve towards self-sustaining oscillations at the loci of gain irregularities. Correspondingly, the spectrum of transient evoked OAEs exhibits sharp peaks. If both the CA gain and the middle-ear forward transfer function are smooth, residual BM oscillations have regular waveforms and extinguish rapidly. In this case no emissions are produced. Finally, and paradoxically albeit consistent with observations, simulating localized damage to the CA results in self-sustaining BM oscillations at the characteristic frequencies (CFs) of the sites adjacent to the damage region, accompanied by generation of spontaneous OAEs. Under these conditions, stimulus-frequency OAEs, with typical modulation patterns, are also observed for inputs near hearing threshold. This approach can be exploited to provide novel diagnostic tools and a better understanding of key phenomena relevant for hearing science.

Stimulus-frequency-emission group delay: a test of coherent reflection filtering and a window on cochlear tuning

This paper tests and applies a key prediction of the theory of coherent reflection filtering for the generation of reflection-source otoacoustic emissions. The theory predicts that reflection-source-emission group delay is determined by the group delay of the basilar-membrane (BM) transfer function at its peak. This prediction is tested over a seven-octave frequency range in cats and guinea pigs using measurements of stimulus-frequency-emission (SFOAE) group delay. A comparison with group delays calculated from published measurements of BM mechanical transfer functions supports the theory at the basal end of the cochlea. A comparison across the whole frequency range based on variations in the sharpness of neural tuning with characteristic frequency (CF) suggests that the predicted relation holds in the basal-most 60% of the cochlea. At the apical end of the cochlea, however, the measurements disagree with neural and mechanical group delays. This disagreement suggests that there are important differences in cochlear mechanics and/or mechanisms of emission generation between the base and apex of the cochlea. Measurements in humans over a four-octave range indicate that human SFOAE group delays are roughly a factor of 3 longer than their counterparts in cat and guinea pig but manifest similar trends across CF. The measurements thus reveal global deviations from scaling whose form appears quantitatively similar in all three species. Interpreted using the theory of coherent reflection filtering, the group delay measurements indicate that the wavelength at the peak of the traveling wave decreases with increasing CF at a rate of roughly 25% per octave in the base of the cochlea. The measurements and analysis reported here illustrate the rich potential inherent in OAE measurements for obtaining valuable information about basic cochlear properties such as tuning.

Limiting frequency of the cochlear amplifier based on electromotility of outer hair cells

Outer hair cells are the critical element for the sensitivity and sharpness of frequency selectivity of the ear. It is believed that fast motility (electromotility) of these cells is essential for this function. Indeed, force produced by outer hair cells follows their membrane potential very closely at least up to 60 kHz. However, it has been pointed out that the cell's receptor potential is attenuated by a low-pass RC circuit inherent to these cells, with the RC roll-off frequencies significantly lower than their operating frequencies. This would render electromotility ineffective in producing force. To address this issue, we assume that multiple degrees of freedom and vibrational modes due to the complex structure of the organ of Corti provide optimal phases for outer hair cells' force to cancel viscous drag. Our derived frequency limit depends on the drag-capacitance product, not directly on the RC time constant. With a reasonable assumption for the viscous drag, the estimated limit is 10-13 kHz, exceeding the RC corner frequency. Our analysis shows that a fast-activating potassium current can substantially extend the frequency limit by counteracting the capacitive current.